The present invention relates to a deep groove ball bearing as a small size ball bearing, extra small ball bearing or a miniature ball bearing, which is incorporated into a bearing device of the business machine, AV home use device, HDD device and the like, and a bearing device using the deep groove ball bearing.
In related art, when a raceway groove 1 formed in a raceway of a deep groove ball bearing is worked, the absolute values of the upper and lower limit values of the groove radius of the raceway groove are selected for each bearing number of the deep groove ball bearing, and the raceway groove is worked to be within the tolerance of those values as shown in FIG. 1. Such working of raceway groove makes possible to prevent the ball from climbing over the shoulder of the raceway and suppress the influence of the groove radius on the wear and life of the ball bearing.
However, not only the groove radius of the raceway groove 1 but also a deformation of an arc profile of the raceway groove 1 affect the bearing functions, such as sound life and wear. In a case where the cross section of the raceway groove 1 is an arc profile having the groove radius as designed in average value, it the arc profile is undulated, the bearing functions are adversely affected by the undulation.
Particularly, the undulation problem of the arc profile of the raceway groove 1 is more serious in the case of the small bearing, such as the small size ball bearing, extra small ball bearing or the miniature ball bearing.
Accordingly, an object of the present invention is to provide a deep groove ball bearing and a bearing device in which the bearing functions are improved by limiting the profile deformation quantity of the raceway groove within specific ranges of values.
To achieve the above object, there is provided a deep groove ball bearing according to a first aspect of the present invention, having an inner ring, an outer ring and a plurality of balls located between the inner ring and the outer ring. In the deep groove ball bearing, a profile deformation quantity xcex94i (mm) of a raceway groove of the inner ring and a profile deformation quantity xcex94o (mm) of a raceway groove of the outer ring are defined by the following equations (1) and (2).
Here, as shown in FIG. 2, the profile deformation quantity means the maximum value of the amplitude of surface waviness (represented by broken line in FIG. 2) along an arc direction of the raceway groove 1 with respect to the arc profile of the raceway groove 1. For example, the profile deformation quantity is the maximum value of the amplitude of the sinusoidal wave shaped waviness.                                           Δ            ⁢                          xe2x80x83                        ⁢            i                    ≦                      36            ⁢                                          (                                  1                                      Ei                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxi                    Ryi                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryi                        Rxi                                            )                                                                                  }                        ⁢                                          Rxi                ·                Ryi                                            Rxi                +                Ryi                                                    ⁢                  
                ⁢        wherein        ⁢                  
                ⁢                              1                          Ei              xe2x80x2                                =                                    1              2                        ⁢                          (                                                                    1                    -                                          vi                      2                                                        Ei                                +                                                      1                    -                                          va                      2                                                        Ea                                            )                                      ⁢                  
                ⁢                  Rxi          =                                    Da              2                        xc3x97                                          dm                -                                  Da                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  α                                            dm                                      ⁢                  
                ⁢                  Ryi          =                                    ri              ·              Da                                                      2                ⁢                ri                            -              Da                                      ⁢                  
                ⁢                              cos            ⁢                          xe2x80x83                        ⁢            α                    =                                    ri              +              ro              -                              (                                  Da                  +                                      c                    /                    2                                                  )                                                    ri              +              ro              -              Da                                                          (        1        )                                                      Δ            ⁢                          xe2x80x83                        ⁢            o                    ≦                      89            ⁢                                          (                                  1                                      Eo                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxo                    Ryo                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryo                        Rxo                                            )                                                                                  }                        ⁢                                          Rxo                ·                Ryo                                            Rxo                +                Ryo                                                    ⁢                  
                ⁢        wherein        ⁢                  
                ⁢                              1                          Eo              xe2x80x2                                =                                    1              2                        ⁢                          (                                                                    1                    -                                          vo                      2                                                        Eo                                +                                                      1                    -                                          va                      2                                                        Ea                                            )                                      ⁢                  
                ⁢                  Rxo          =                                    Da              2                        xc3x97                                          dm                +                                  Da                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  α                                            dm                                      ⁢                  
                ⁢                  Ryo          =                                    ro              ·              Da                                                      2                ⁢                ro                            -              Da                                      ⁢                  
                ⁢                              cos            ⁢                          xe2x80x83                        ⁢            α                    =                                    ri              +              ro              -                              (                                  Da                  +                                      c                    /                    2                                                  )                                                    ri              +              ro              -              Da                                                          (        2        )            
where
dm: pitch circle diameter (mm)
Da: ball diameter (mm)
c: diameter clearance (mm)
ri: radius (mm) of the raceway groove of the inner ring
ro: radius (mm) of the raceway groove of the outer ring
Ei: Young""s modulus of the inner ring
xcexdi: Poisson""s ratio of the inner ring
Eo: Young""s modulus of the outer ring
xcexdo: Poisson""s ratio of the outer ring
Ea: Young""s modulus of the ball
xcexda: Poisson""s ratio of the ball
The diameter clearance xe2x80x9ccxe2x80x9d is two times as large as a radial internal clearance.
The validity of the equations (1) and (2) will be described hereunder. Empirically, if a waviness of the raceway groove profile takes a sinusoidal wave in shape, a waviness length is approximately ⅓ as long as an arc length of the raceway groove.
Where a waviness length of a raceway groove profile of a ball bearing of the bearing number 696 (inner diameter=6 mm; outer diameter=15 mm; width=5 mm, bearing pitch circle diameter (dm)=10.5 mm; ball diameter=2.8 mm; curvature radius ratio of the inner ring groove=54%, and curvature radius ratio of the outer ring groove=56%) is assumed to be ⅓ as long as the groove arc length, a maximum surface pressure increases in accordance with the profile deformation quantity as shown in FIG. 3. That is, the maximum surface pressure increases in accordance with the presence of the waviness. In this case, an axial load is 6.3N, which is the pre-load usually used.
In FIG. 3, the horizontal axis represents a distance from the groove shoulder (see FIG. 1). Where the length of the waviness is ⅓ as long as the groove arc length, a contact position with the ball is located at the groove bottom and near the peak of the wave of the waviness.
As seen from FIG. 3, as the profile deformation quantity increases, the contact area of the raceway groove with the ball becomes narrow, and a maximum value Pmax of the contact surface pressure increases.
In the case of the small size ball bearing, extra small ball bearing or the miniature bearing, it is known and confirmed that when the maximum value Pmax of the contact surface pressure exceeds 1.6 GPa, abnormal phenomenon, such as an early minute wear or sound occur (see FIG. 10).
The surface pressure of a small ball bearing of the bearing number 696 was analyzed. Calculation was made about a variation of the maximum value of the contact surface pressure when the profile deformation quantity xcex94 is varied. The calculation results are shown in FIGS. 4 and 5.
In FIGS. 4 and 5, the horizontal axis represents xcex94/xcex4o, which has not the dimension for clarifying a magnitude of the profile deformation quantity xcex94. xcex4o is an elastic approaching quantity (Hertzian elastic approaching quantity) when the raceway groove is not deformed in its profile or when no profile deformation is present.
From FIGS. 4 and 5, it was found that when the ratio xcex94/xcex4o of the inner ring is 2.55 or above, and that of the outer ring is 8.30 or above, the maximum value Pmax of the contact surface pressure exceeds 1.6 GPa. Accordingly, if the profile deformation quantity is selected so as to satisfy
xcex94ixe2x89xa62.55xc2x7xcex4o 
xcex94oxe2x89xa68.30xc2x7xcex4o, 
then the early wear and the like are not affected by the profile deformation even if the profile deformation occurs in the raceway groove.
The Hertzian elastic approaching quantity between the rolling element and the surface of the raceway when no profile deformation is present may approximately be expressed by the following equations (3) and (4).                               δ          ⁢                      xe2x80x83                    ⁢          i                =                  8          ⁢                                    (                              1                                  Ei                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxi                  Ryi                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryi                      Rxi                                        )                                                                        }                    ⁢                                    Rxi              ·              Ryi                                      Rxi              +              Ryi                                ⁢                                    (                              P                ⁢                                  xe2x80x83                                ⁢                max                ⁢                                  xe2x80x83                                ⁢                i                            )                        2                                              (        3        )                                          δ          ⁢                      xe2x80x83                    ⁢          o                =                  8          ⁢                                    (                              1                                  Eo                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxo                  Ryo                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryo                      Rxo                                        )                                                                        }                    ⁢                                    Rxo              ·              Ryo                                      Rxo              +              Ryo                                ⁢                                    (                              P                ⁢                                  xe2x80x83                                ⁢                max                ⁢                                  xe2x80x83                                ⁢                o                            )                        2                                              (        4        )            
where Pmaxi and Pmaxo are the maximum surface pressure values of the inner and outer raceways.
The maximum surface pressure values Pmaxi and Pmaxo when the deep groove ball bearing as axially pre-loaded is not deformed in profile, are selected in design in the following manner. Those values indicate the most stringent range of values presented when the design tolerance is taken into consideration.
Pmaxi (Inner Ring Side):
1.18xcx9c1.47 GPa (120xcx9c150 kgf/mm2)
Pmaxo (Outer Ring Side):
1.03xcx9c1.18 GPa (105xcx9c120 kgf/mm2)
The maximum surface pressure values are determined in the following way.
For the maximum surface pressure value Pmaxi, the center value 1.32 GPa of the above range was used.
A load to the rolling element was 9.6N. For the maximum surface pressure value Pmaxo under this load, the value 1.16 GPa was used since a surface pressure at which the rolling element load is 9.6N, is 1.16 GPa.
When this value is substituted into the equations (3) and (4), then equations (5) and (6) are obtained. Accordingly, it the maximum profile deformation quantity is selected to be within a range of values which satisfies the equations (5) and (6), the adverse effects owing to the waviness, such as early wear, are prevented.                                           Δ            ⁢                          xe2x80x83                        ⁢            i                    ≦                                    2.55              ·              8              ·                              1.32                2                                      ⁢                                          (                                  1                                      Ei                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxi                    Ryi                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryi                        Rxi                                            )                                                                                  }                        ⁢                                          Rxi                ·                Ryi                                            Rxi                +                Ryi                                                    =                  36          ⁢                                    (                              1                                  Ei                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxi                  Ryi                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryi                      Rxi                                        )                                                                        }                    ⁢                                    Rxi              ·              Ryi                                      Rxi              +              Ryi                                                          (        5        )                                                      Δ            ⁢                          xe2x80x83                        ⁢            o                    ≦                                    8.30              ·              8              ·                              1.16                2                                      ⁢                                          (                                  1                                      Eo                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxo                    Ryo                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryo                        Rxo                                            )                                                                                  }                        ⁢                                          Rxo                ·                Ryo                                            Rxo                +                Ryo                                                    =                  89          ⁢                                    (                              1                                  Eo                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxo                  Ryo                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryo                      Rxo                                        )                                                                        }                    ⁢                                    Rxo              ·              Ryo                                      Rxo              +              Ryo                                                          (        6        )            
The relation between the ratio (xcex94/xcex4o) and the maximum value Pmax of the contact surface pressure in a small ball bearing of the bearing number 684 (inner diameter=4 mm, outer diameter =9 mm; width=2.5 mm, bearing pitch circle diameter (dm) is 6.35 mm; ball diameter=1.6 mm; curvature radius ratio of the inner ring groove=56%, and curvature radius ratio of the outer ring groove=56%) was obtained for the inner ring and the outer ring. The results were as shown in FIGS. 6 and 7.
From FIGS. 6 and 7, it was found that when the ratio xcex94/xcex4o of the inner ring is 3.7 or above, and that of the outer ring is 10.35 or above, the maximum value Pmax of the contact surface pressure exceeds 1.6 GPa. Accordingly, the profile deformation quantity is selected so as to satisfy
xcex94ixe2x89xa63.7xc2x7xcex4o 
xcex94oxe2x89xa610.35xc2x7xcex4o 
In the case of the bearing of the bearing number 684, the maximum surface pressure values Pmaxi and Pmaxo when no profile deformation is present are 1.32 GPa (which is the above-mentioned center value and corresponds to 2.45N of the rolling element load) for the inner ring side, and 1.08 GPa (which corresponds to 2.45N of the rolling element load) for the outer ring side.
Then, if those values are substituted into the equations (3) and (4), then equations (7) and (8) are obtained. Accordingly, if the maximum profile deformation quantity is selected to be within a range of values which satisfies the equations (7) and (8) the adverse effects owing to the waviness, such as early wear, are prevented.                                           Δ            ⁢                          xe2x80x83                        ⁢            i                    ≦                                    3.70              ·              8              ·                              1.32                2                                      ⁢                                          (                                  1                                      Ei                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxi                    Ryi                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryi                        Rxi                                            )                                                                                  }                        ⁢                                          Rxi                ·                Ryi                                            Rxi                +                Ryi                                                    =                  52          ⁢                                    (                              1                                  Ei                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxi                  Ryi                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryi                      Rxi                                        )                                                                        }                    ⁢                                    Rxi              ·              Ryi                                      Rxi              +              Ryi                                                          (        7        )                                                      Δ            ⁢                          xe2x80x83                        ⁢            o                    ≦                                    10.35              ·              8              ·                              1.08                2                                      ⁢                                          (                                  1                                      Eo                    xe2x80x2                                                  )                            2                        ⁢                          (                              1.0003                +                                  0.5968                  ⁢                                      Rxo                    Ryo                                                              )                        ⁢                          {                              1.5227                +                                  0.6023                  ⁢                                      ln                    ⁡                                          (                                              Ryo                        Rxo                                            )                                                                                  }                        ⁢                                          Rxo                ·                Ryo                                            Rxo                +                Ryo                                                    =                  97          ⁢                                    (                              1                                  Eo                  xe2x80x2                                            )                        2                    ⁢                      (                          1.0003              +                              0.5968                ⁢                                  Rxo                  Ryo                                                      )                    ⁢                      {                          1.5227              +                              0.6023                ⁢                                  ln                  ⁡                                      (                                          Ryo                      Rxo                                        )                                                                        }                    ⁢                                    Rxo              ·              Ryo                                      Rxo              +              Ryo                                                          (        8        )            
The values of the right side of the equations (7) and (8) are larger than those of the right side of the equations (1) and (2). Accordingly, in the deep groove ball baring according to the first aspect of the present invention, the profile deformation quantities xcex94i and xcex94o of the inner and outer raceways are selected in value so as to satisfy the equations (1) and (2), so that the maximum surface pressure produced in the raceway groove of each inner and outer rings may always be kept at 1.6 GPa or lower.
Preferably, in the deep groove ball bearing of the present invention, a pitch circle diameter of the bearing is 21 mm or smaller.
As will be described later, it was found that where the bearing pitch circle diameter is 21 mm or smaller, the adverse effects owing to the waviness, such as the early wear, are present unless the profile deformation quantity is actively controlled as mentioned above. Therefore, in the deep groove ball bearing of the present invention, the pitch circle diameter is selected to be 21 mm or smaller.
Further, to achieve the object of the present invention, there is provided a deep groove ball bearing according to a second aspect of the present invention, having a plurality of balls located between an inner ring and an outer ring, wherein a pitch circle diameter of the bearing is 21 mm or smaller, and a profile deformation quantity of a raceway groove of the inner ring is 2 xcexcm or smaller.
In the case of the bearing whose pitch circle diameter is within 7.5 mm to 21 mm, if the profile deformation quantity of the raceway groove of the inner ring is selected to be 2 xcexcm or smaller, the adverse effects owing to the waviness, such as the early wear, are prevented. Therefore, in the deep groove ball bearing of the present invention, the profile deformation quantity of the raceway groove of the inner ring is selected to be 2 xcexcm or smaller (see FIG. 14).
Preferably, in the deep groove ball bearing, the pitch circle diameter of the bearing is 5.5 mm to 7.5 mm, and the profile deformation quantity of the raceway groove of the inner ring is 1.5 xcexcm or smaller.
In the case of the bearing whose pitch circle diameter is within 5.5 mm to 7.5 mm, if the profile deformation quantity of the raceway groove of the inner ring is selected to be 1.5 xcexcm or smaller, the adverse effects owing to the waviness, such as the early wear, are prevented. Therefore, in the deep groove ball bearing of the present invention, the profile deformation quantity of the raceway groove of the inner ring is selected to be 1.5 xcexcm or smaller (see FIG. 14).
More preferably, the pitch circle diameter of the bearing is 4.0 mm to 5.5 mm, and the profile deformation quantity of the raceway groove of the inner ring is 1 xcexcm or smaller.
In the case of the bearing whose pitch circle diameter is within 4.0 mm to 5.5 mm, it the profile deformation quantity of the raceway groove of the inner ring is selected to be 1.0 xcexcm or smaller, the adverse effects owing to the waviness, such as the early wear, are prevented. Therefore, in the deep groove ball bearing of the present invention, the profile deformation quantity of the inner raceway groove is selected to be 1.0 xcexcm or smaller (see FIG. 14).
Further, to achieve the object of the present invention, there is provided a bearing device using any of the deep groove ball bearings mentioned above. In the bearing device, the bearing has an internal clearance when the bearing stands alone, and the bearing is assembled into the bearing device while being pre-loaded.
Any of the deep groove ball bearings is pre-loaded and then is used with a predetermined surface pressure being applied thereof.
The bearing device may be incorporated into the business machine, AV home use device, and HDD device.
Other objects, advantages and features of the invention will be apparent when carefully reading the detailed description of the invention in connection with the accompanying drawings.